For several years now I have been trying to make my own gear cutting hobs. The Eureka relieving device shown in Workshop Practice Series 17 is what I started with. They started with a picture of the Balzer device and reverse engineered it.
I followed the plans closely because I had no idea how it worked.
My first change was to make it longer so a hob blank would fit. The hobs for diametral pitch have a lead which is a factor of pi. I used a 42t and a 44t gear together to make 22/7 pi.
This makes the half nuts unusable like metric conversion gears do.To do plain turning on hob blanks the tool is pulled back and the lathe is reversed with the half nuts engaged for the next pass.
The problem with the Eureka relieving device is that it drives through a ratchet so it loses place when you reverse it.
I was able to relieve hobs with it but it was very tedious since the tool had to be adjusted to pick up the thread each pass.
My solution is to use a pattern thread on the reliever and a half nut connected to the lathe saddle to drive the carriage.
Now the lathe is only reversed while cutting the pattern thread and half nut. A different pattern and nut are needed for each thread pitch.
Plain turning the hob and relieving it are all done with the pattern thread so there is no need to reverse the lathe. The pattern thread half nut always engages correctly.
A plain arbor that matches the reliever arbor is used. Both have a keyway to index the pattern thread and hob blank.
There is a better description of the Balzer Relieving device atpages 26 to 28 which seems to be the origin of this tool in 1896 or so.
Taylor's 1906 patent 817885 is a paraphrase of Balzer's design.
Balzer has a 1895 patent 535127 for a reliever with no ratchets and a trick gear but it was not the design that he manufactured.
Here is my hob reliever on U-tube. It is not as complicated as building a backing off lathe but it can't do small hobs for cutting worm wheels.So far I can't get U-tube search to find it.
Best Regards Charlie